
7.2.7.2 ring operations (plural)
+
 construct a tensor product
of two
algebras and over the ground field. Let, e.g.,
,
and
be two
algebras, then
is defined to be the algebra
,
,
.
Concerning the ground fields
resp.
of
resp.
, take the
following guidelines for
into consideration:
 Neither
nor
may be
or
.
 If the characteristic of
and
differs, then one of them must be
.
 At most one of
and
may have parameters.
 If one of
and
is an algebraic extension of
it may not be defined by a
charstr of type (p^n,a) .
One can create a ring using ring(list) , see also ringlist .
Example:
 LIB "ncalg.lib";
def a = makeUsl2(); // U(sl_2) in e,f,h presentation
ring W0 = 0,(x,d),dp;
def W = Weyl(); // 1st Weyl algebra in x,d
def S = a+W;
setring S;
S;
==> // coefficients: QQ
==> // number of vars : 5
==> // block 1 : ordering dp
==> // : names e f h
==> // block 2 : ordering dp
==> // : names x d
==> // block 3 : ordering C
==> // noncommutative relations:
==> // fe=efh
==> // he=eh+2e
==> // hf=fh2f
==> // dx=xd+1

